Anode Sheath and Double Layer Solutions with Ionization

POSTER

Abstract

When an electrode in a plasma is biased more positive than the plasma potential it attracts electrons and repels ions forming a region of negative space charge (electron sheath). Ballistic electrons moving towards this anode gain energy equal to the difference in electrostatic potential energy, $\Delta \phi=\phi(x) -\phi_{plasma}$, with a maximum of $\phi_{anode}-\phi_{plasma}$. When $\phi_{anode}$ is large enough, electrons can gain enough energy to ionize neutral atoms through electron impact ionization. This leads to a layer of increased ion density near the anode, which can exceed the local electron density at large enough anode biases forming a double layer. We model the sheath potential profile using Poisson's equation with a fluid model for the electron density in the case without ionization and formulate an integral equation for the case with ionization where the ion density depends on an integral from $\phi(x)$ to $\phi_{anode}$. An analytic form of the sheath electric field is obtained for the case without ionization and we demonstrate that it asymptotically agrees with the Child-Langmuir solution. We numerically obtain double layer solutions when including ionization and show that the potential profile expands beyond that of the Child-Langmuir solution.

Authors

  • Brett S. Scheiner

    Department of Physics and Astronomy, University of Iowa

  • John Verboncoeur

    Missouri University of Science and Technology, Los Alamos National Laboratory, Tsinghua University, University of Manchester, Kyoto University, FOM Institute DIFFER, Edisonbaan 14, 3439 MN Nieuwegein, Nagoya University, Tokyo Electron Ltd, Princeton University, The George Washington University, IMEC, The Open University, Oxford Instruments Plasma Technology, UK, York Plasma Institute, University of York, UK, Eindhoven University of Technology, The Netherlands, Institute for Plasma and Atomic Physics, Ruhr-University Bochum, 44780 Bochum, Germany, Department of Physics, West Virginia University, Morgantown, WV 26506, Department of Physics, University of Alberta, Canada, None, Hokkaido University, Kyushu University, Sepuluh Nopember Institute of Technology, University of Saskatchewan, Canada, The Ohio State Univesity, Air Force Research Laboratory, University of California, Berkeley, Aurtas International, Inc., University of Colorado-Boulder, Tokyo Institute of Technology, NU Global, Tokyo Inst of Tech - Tokyo, Meijo University, Hokkaido Univ., National Defense Academy, Dalian University of Technology, Hiden Analytical, Queen's University Belfast, Wesleyan University, CFD Research Corporation, Princeton Plasma Phys Lab, General Electric Research, Niskayuna, NY, Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, Budapest, Hungary, Electrical Engineering and Computer Science, U. Michigan, UCLA Department of Physics, Physics Department, Badji Mokhtar University, Annaba, Algeria, Flinders University, James Cook University, Universidad Nacional Aut\'onoma de M\'exico, CNRS and Univ. Toulouse, Drake Univ., Tohoku University, Tokyo Electron Limited, ZIK plasmatis at INP Greifswald, INP Greifswald, ZIK plasmatis at INP Greifswald, TU Eindhoven, Tokyo Metropolitan University, Tokyo Institute of Tech., York Plasma Institute, University of York, Fukuoka University, Charles University Prague, Green Chemistry Centre of Excellence, University of York, Now at the University of Liverpool, Texas A\&M University, The University of Tokyo, National Institute for Fusion Science, Old Dominion University, University of Paul Sabatier, University of Montreal, Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, The Ohio State University, Victor Technologies, West Lebanon, University of Liverpool, Institute of Theoretical Electrical Engineering, Ruhr University Bochum, Eindhoven University of Technology, CNRS and Univ Toulouse, Centrum Wiskunde \& Informatica and Eindhoven University of Technology, The Netherlands, Tsinghua University, China, LAPLACE, CNRS and University of Toulouse, Natl Fusion Res Inst, National Fusion Research Institute, Spectral Energies, LLC., UES, Inc., Hanyang University, Seoul University, SEMES, Department of Electrical Engineering, Hanyang University, Seoul, 133-791, Republic of Korea, Department of Nanoscale Semiconductor Engineering, Hanyang University, Seoul, 133-791, Republic of Korea, Department of Nanoscale Semiconductor Engineering, Hanyang University, Seoul 133-791, South Korea, Department of Electrical Engineering, Hanyang University, Department of Nanoscale Semiconductor Engineering, Hanyang University, University of Wisconsin-Madison, HuaZhong University, University of Antwerp, Universit\'e d'Orleans, Applied Materials, Silicon Systems Group, Varian Semiconductor Equipment, University of Wisconsin-Madison, Department of Engineering Physics, Department of Physics and Astronomy, University of Iowa, Department of Electrical Engineering, Hanyang University, Seoul 133-791, South Korea, SPbGU, SPbU SES, WVU, Stanford University, Ruhr University Bochum, OSRAM AG, Berlin, General Electric Reserach, Wigner Research Center for Physics, Budapest, West Virginia University, Morgantown, York Plasma Institute, Department of Physics, University of York, York, YO10 5DD, Centre for Plasma Physics, Queen's University Belfast, Belfast, BT7 1NN, GREMI/CNRS/Universit\'e d'Orleans, CNRS/Universit\'e d'Orleans, ZIK plasmatis @ INP Greifswald, Kwangwoon University, Drexel University, A.J. Drexel Plasma Institute, YCR Cancer Research Unit, Department of Biology, University of York, UK, York Plasma Institute, Department of Physics, University of York, UK, National Institute of Advanced Industrial Science and Technology, Japan, Sandia National Laboratories, ZIK plasmatis at the INP Greifswald e.V., Laboratoire de Physique des Gaz et des Plasmas (LPGP), CNRS \& Universit\'e Paris-Sud, Queens University Belfast, University of York, University of Michigan, Michigan State University